... and beyond

(f○g)(x)=√(1-3x²)/(2x-8) and (g○f)(x)=(1-3x²)/(3-2x²) . How to find f(g(4))?

1 Answer

#(f@g)(x)# is an alternate way of writing #f(g(x))# and is undefined when #x=4#

Explanation:

#f(g(x))# is the same as #(f@g)(x)#

So#f(g(4))# is the same as #(f@g)(4)#

But#(f@g)(x) = sqrt(1-3x^2)/(2x-8)##color(white)("XXXX")##color(white)("XXXX")#...or #sqrt((1-3x^2)/(2x-8))##color(white)("XXXX")##color(white)("XXXX")#it's hard to guess the range of the root symbol#color(white)("XXXX")##color(white)("XXXX")#and doesn't make any difference in this case, since...
When #x=4##color(white)("XXXX")#we have an attempt to divide by zero#color(white)("XXXX")#which is undefined.